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A bivariate, multimodal distribution Figure 4. A non-example: a unimodal distribution, that would become multimodal if conditioned on either x or y. In statistics, a multimodal distribution is a probability distribution with more than one mode (i.e., more than one local peak of the distribution).
The Beta distribution on [0,1], a family of two-parameter distributions with one mode, of which the uniform distribution is a special case, and which is useful in estimating success probabilities. The four-parameter Beta distribution, a straight-forward generalization of the Beta distribution to arbitrary bounded intervals [,].
A mode of a continuous probability distribution is often considered to be any value x at which its probability density function has a locally maximum value. [2] When the probability density function of a continuous distribution has multiple local maxima it is common to refer to all of the local maxima as modes of the distribution, so any peak ...
Median: the value such that the set of values less than the median, and the set greater than the median, each have probabilities no greater than one-half. Mode: for a discrete random variable, the value with highest probability; for an absolutely continuous random variable, a location at which the probability density function has a local peak.
If there is a single mode, the distribution function is called "unimodal". If it has more modes it is "bimodal" (2), "trimodal" (3), etc., or in general, "multimodal". [2] Figure 1 illustrates normal distributions, which are unimodal. Other examples of unimodal distributions include Cauchy distribution, Student's t-distribution, chi-squared ...
The split normal distribution has been used mainly in econometrics and time series. A remarkable area of application is the construction of the fan chart, a representation of the inflation forecast distribution reported by inflation targeting central banks around the globe. [7] [11]
This means that if a data point has either a categorical or multinomial distribution, and the prior distribution of the distribution's parameter (the vector of probabilities that generates the data point) is distributed as a Dirichlet, then the posterior distribution of the parameter is also a Dirichlet. Intuitively, in such a case, starting ...
The multinomial distribution models the outcome of n experiments, where the outcome of each trial has a categorical distribution, such as rolling a k-sided die n times. Let k be a fixed finite number. Mathematically, we have k possible mutually exclusive outcomes, with corresponding probabilities p 1, ..., p k, and n independent trials.